question_answer

Consider the following statements: For non-empty sets. A, B and C

1. \[A-(B-C)=(A-B)\cup C\]

2. \[A-(B\cup C)=(A-B)-C\]

Which of the statements given above is/are correct?

A) 1 only              

B) 2 only

C) Both 1 and 2                 

D) neither 1 nor 2

Correct Answer: B

Solution :

[b]Let there be three non-empty, non-overlapping sets; inside a universal set U. This creates 8 regions marked as: a, b, c, d, e, f, g, h. Statement1: \[A-(B-C)=(A-B)\cup C\] LHS represent region a, RHS represent a, d, g. Hence, this is not correct. Statement2: \[A-(B\cup C)=(A-B)-C\] LHS represents, region ?a? RHS also represent a. Hence, only statement 2 is correct.